An HTTP proxy integration enables you to connect an API route to a publicly routable HTTP endpoint. With this integration type, API Gateway passes the entire request and response between the frontend and the backend.

This is very useful for example if you have an old API that you are going to gradually migrate and you want to proxy requests to the old api ( until you can replace the HTTP Proxy Integration with a Lambda Integration or First Class integration to other services)

Mock integrations are a nice way to provide mocked implementation, for example if your backend team is not yet ready with a specific resource or method. I talked about it in this post